Active Control of Translating Media With Arbitrarily Varying Length

[+] Author and Article Information
W. D. Zhu

Department of Mechanical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250e-mail: wzhu@umbc.edu

J. Ni

Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030

J. Huang

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong

J. Vib. Acoust 123(3), 347-358 (Feb 01, 2001) (12 pages) doi:10.1115/1.1375809 History: Received February 01, 2000; Revised February 01, 2001
Copyright © 2001 by ASME
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Grahic Jump Location
Schematic of a horizontally (a) or vertically (b) translating beam with an attached mass-spring at x=l(t) subject to a pointwise control force uf(t) and/or moment um(t) at x=θ(t)
Grahic Jump Location
Schematic of a vertically translating string with an attached mass-spring at x=l(t) subject to a pointwise control force uf(t) at x=θ(t)
Grahic Jump Location
The tip responses and energies of vibration of uncontrolled translating beams with and without end mass during extension (a) and retraction (b). Solid, me*=0.2; dashed, me*=0.
Grahic Jump Location
The tip responses and energies of vibration of uncontrolled and controlled translating beams without end mass during extension (a) and retraction (b). Dash-dotted, uncontrolled; dotted, domain force control with Kf*=0.2 and θ*(t*)=l*(t*)−0.1; solid, boundary force control with Kf*=0.2; dashed, boundary moment control with Km*=0.2.
Grahic Jump Location
The effect of the control gain in the boundary force control law (35) on the response of the translating beam without end mass. Dependences of the average energy of vibration on the control gain Kf* during extension and retraction are shown in (a) and (b), respectively. Under various control gains, the energy of vibration and the tip displacement are shown in (c) and (e) during extension, and (d) and (f) during retraction. Solid in (c) and (e), Kf*=1.22 (optimal); solid in (d) and (f), Kf*=1.26 (optimal); dashed in (c)–(f), Kf*=5; dotted in (c)–(f), Kf*=0.2; dash-dotted in (c)–(f), Kf*=1000.



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